Yes, they are a face/eye/tooth hazard. There are several ways to secure them but this is a common one...
It is hard to expalin but you tie a clip on the end of the bungie, before you secure it to the trap line (adjustable line, not the metal wire) this way you can secure the trap ring.
Sorry for the crude drawing.. but this is a picture (the clip is done in red so you can see it).
--
Andrew Scott
Mystère 5.5
--